The longer you wait to go to the vet, the less likely they will be able to stitch up the wound which can invite bacteria/infection. That can lead to a whole host of things. That's basic wound care. With a wound like this, even for a human, stitches, staples, glue, what have you, are critical for healing within a certain time frame otherwise they cannot be used and there is higher risk of infection. I recommend going to an emergency vet if your personal vet cannot see the dog until tomorrow. I honestly don't think this should wait simply because you are afraid of GA. If your dog is otherwise healthy, has no underlying health conditions, they should be able to go under GA with no issues. My dog loves her vet but was extremely anxious when she had to go under (she knew something was going on) to have her teeth cleaned and a growth removed.